One of the problems which continues to exist is the size of the transfer devices utilized in treating blood with a resultant large priming volume. It has been found that maximum transfer will occur with a relatively thin blood stream, but the difficulty has been in forming the transfer devices so as to provide for such generally laminar flow of blood while assuring constant flow, due to collapse of the material defining the passages. Another desire has been to form a dialyzer of such a size that it could properly be attached to or even incorporated within the body for use over longer periods of time than is presently feasible.